How to Think Clearly about the Central Limit Theorem

The Central Limit Theorem (CLT) is one of the most important theorems in statistics, and it is often introduced to social sciences researchers in an introductory statistics course. However, the recent replication crisis in the social sciences prompts us to investigate just how common certain misconceptions of statistical concepts are. The main purposes of this paper are to investigate the misconceptions of the CLT among social sciences researchers and to address these misconceptions by clarifying the definition and properties of the CLT in a manner that is approachable to social science researchers. As part of our paper, we conducted a survey to examine the misconceptions of the CLT among graduate students and researchers in the social sciences. We found that the most common misconception of the CLT is that researchers think the CLT is about the convergence of sample data to the normal distribution. We also found that most researchers did not realize that the CLT applies to both sample means and sample sums, and that the CLT has implications for many common statistical concepts and techniques. Our paper addresses these misconceptions of the CLT by explaining the preliminaries needed to understand the CLT, introducing the formal definition of the CLT, and elaborating on the implications of the CLT.We hope that through this paper, researchers can obtain a more accurate and nuanced understanding of how the CLT operates as well as its role in a variety of statistical concepts and techniques.